An Iterative Parallel Solver in GPU Applied to Frequency Domain Linear Water Wave Problems by the Boundary Element Method

Abstract

In this paper a parallel iterative solver based on the Generalized Minimum Residual Method (GMRES) with complex-valued coefficients is explored, with applications to the Boundary Element Method (BEM). The solver is designed to be executed in a GPU (Graphic Processing Unit) device, exploiting its massively parallel capabilities. The BEM is a competitive method in terms of reduction in the number of degrees of freedom. Nonetheless, the BEM shows disadvantages when the dimension of the system grows, due to the particular structure of the system matrix. With difference to other acceleration techniques, the main objective of the proposed solver is the direct acceleration of existing standard BEM codes, by transfering to the GPU the solver task. The CUDA programming language is used, exploiting the particular architecture of the GPU device for complex-valued systems. To explore the performances of the solver, two linear water wave problems have been tested: the frequency-dependent added mass and damping matrices of a 3D floating body, and the Helmholtz equation in a 2D domain. A NVidia GeForce GTX 1080 graphic card has been used. The parallelized GMRES solver shows reductions in computing times when compared with its CPU implementation.